But the club was accused of seeking to avoid public scrutiny over the remarks, which were made two weeks ago but only emerged on Sunday when they were leaked to a tabloid newspaper.

Video footage of the conversation between Moyes and the BBC Radio 5 Live reporter Vicki Sparks showed the Scot reacting to a question he did not like following Sunderland’s goalless draw with Burnley on 18 March.

Believing the cameras were off, he said: “You were just getting a wee bit naughty at the end there, so just watch yourself. You still might get a slap even though you’re a woman. Careful the next time you come in.”

Moyes and the BBC said he had apologised to Sparks, who had accepted the apology, and the manager made further expressions of regret in his press conference before Tuesday’s Premier League match at Leicester City.

But the row refused to die down as domestic violence charities said the Premier League manager’s comments reflected a “rampant sexism” in football and a cover-up culture reminiscent of the Adam Johnson case last year.

Polly Neate, the chief executive of Women’s Aid, said: “The ingrained sexism at the heart of Mr Moyes’ remark represents something much darker; it is a cornerstone of a culture that condones violence against women.”

Neate said two women were killed by a partner or ex-partner every week on average in England and Wales and society could not be “complacent about remarks like these from influential men”.

“But the power and platform of football can be part of the solution to ending violence against women,” she said. “We urge the FA to act swiftly and take this opportunity to send out a clear and strong message to the footballing community – fans, clubs and players – that there is no place for sexism and misogyny in modern football.”

The FA has written to Sunderland to request Moyes’s observations on his remarks and is expecting a reply this week before deciding what action to take, if any.

The FA’s independent regulatory commission could hand down a five-game suspension, meaning Moyes may be forced to miss the final games of Sunderland’s battle to avoid relegation from the Premier League. He could also face a fine and have to undertake an educational programme, according to the FA’s rulebook.

Jonathan Copping, a sports lawyer at solicitors’ firm Bold Burdon, who has advised clients during regulatory commission hearings, said Moyes’s remarks appeared to be a breach of Rule E3(2) of FA rules, meaning they were an “aggravated breach” of threatening language, which brings the game into disrepute.

Copping said: “The FA, as the governing body in this country, has to be seen to be taking steps forward in relation to sexism and threats of violence and when people in the public eye are making comments like that it has to act accordingly.”

Clare Phillipson, director of Wearside Women in Need, questioned why Moyes’s remarks only came to light on Sunday. The club has said that Moyes “immediately” recognised he had done wrong and alerted Martin Bain, the chief executive, and apologised privately to Sparks.

But Phillipson said the incident had echoes of Sunderland’s handling of Adam Johnson, the convicted sex offender whom the club continued playing despite knowing he had privately admitted kissing and sending sexually charged text messages to a 15-year-old schoolgirl. Criticism of the club led Margaret Byrne, Sunderland’s then chief executive, to quit over the affair.

“We’ve had Adam Johnson and now we’ve got this. Clearly people intended it to not go public, that it would all be kept behind closed doors – again – and not dealt with. They were clearly hoping to avoid any public scrutiny,” Phillipson said.

“They’re a business and they’re trying to keep it running, and it’s a very important part of the local economy, but if their business model involves rampant sexism then they’re going to be turning off a fair number of paying customers.”

The controversy has shone an uncomfortable spotlight on relations between top-flight football clubs and the media organisations that cover them. Two journalists claimed publicly on Tuesday that Moyes had made similar disparaging remarks to or about women journalists but the incidents were never publicised at the time.

One senior sports journalist said: “These organisations are so scared of upsetting clubs and being banned – and she was a freelancer, she couldn’t afford to be banned – I think they probably decided to keep it quiet but then somebody’s obviously leaked it to the Star. It’s extraordinary and sad that it took somebody to leak it.”

A Sunderland AFC spokeswoman said: “The exchange between the manager and a BBC reporter was wholly unacceptable and such actions are not condoned or excused in any way.

“David recognised this immediately, proactively bringing the matter to the attention of the CEO and apologising to the reporter. The club also spoke with both a senior figure at the BBC and the reporter personally, expressing its profound regret over what had occurred.

“The matter was treated with the utmost seriousness from the outset and the swift and decisive action taken by the club and the manager at the time ensured that it was resolved to the satisfaction of the reporter and the BBC, which was the priority.

“With both the BBC and the reporter agreeing that appropriate action had been taken at the time, the club continues to fully support David in his role as manager of Sunderland AFC.”